ANSWER: The correct answer is \(R(S(x))=x\).
Explanation
The composition of a function of \(x\) and its inverse will produce the independent variable \(x\).
For instance, let \(f(x)=2x\).
The inverse of this function is \(f^{-1}(x)=\frac{x}{2}\).
If we compose these two functions, we will obtain;
\((f\circ f^{-1})(x)=f(f^{-1}(x))\)
This means we have to substitute the whole inverse function in to the function itself.
\((f\circ f^{-1})(x)=f(f^{-1}(x))=2(\frac{x}{2})=x\)
The other way round will also produce the same result.
Thus;
\((f^{-1}\circ f(x)=f^{-1}(f(x))=(\frac{2x}{2})=x\)
This does not only apply to the given example it applies to all functions and their inverse.
